A key feature of imperfectly competitive markets is the presence of differentiated products that cater specifically for the heterogeneity of consumer tastes. Identifying substitution patterns between such products in response to changes in price and other marketing variables is central to an understanding and estimation of consumer demand. A popular modelling framework is the continuous choice Almost Ideal Demand System (AIDS) of Deaton and Muellbauer (1980). In this paper, we develop the static functional form of the AIDS to include additional marketing mechanics and provide a dynamic generalisation based on the Unobserved Component Model (UCM) and state-space modelling techniques. 

The proposed model improves on conventional dynamic econometric share models in three key ways. Firstly, the model structure explicitly separates the transitory and permanent components of each brand share. This allows a formal analysis of their time series properties that is statistically superior to the standard unit root tests generally employed in the literature. Secondly, the parameters of the marketing variables are directly interpretable as short-run demand effects: parameter estimates in standard short-run models formulated in first differences are not readily interpretable in this way, whereas parameters based on short-run models using lagged dependent variables are biased. Finally, the extracted permanent components can be used to assess the long-run impact of marketing activity. 

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